Torsional Shear Strength - ELASTIC CONSTANTS


Within elastic limit the stress is directly proportional to strain. It is the statement of Hooke's law and is true for direct tensile or compressive stress and strain as well as for shearing involving torsional shearing strain and stress. The ratio of direct stress to  direct strain is explained as modulus of elasticity as E and the ratio of shearing stress and  shearing strain is explained as modulus of rigidity as g. Both the module is called elastic constants. For isotropic material G and E are associated along with Poisson's ratio

                                                                          G = E/{2(I + v)}

Poisson's ratio is the ratio of transverse to longitudinal strains simply magnitude is yet another elastic constant. If stress s acts in three directions at a point this is called volumetric stress and produces volumetric strain. The ratio of volumetric stress to volumetric strain according to Hooke's law is a constant, called bulk modulus and denoted by K.  It is significant to remember that out of four elastic constants, for an isotropic material only two are independent and another two are dependent. Hence K can also be expressed as function of any of two constants.

                                                                          K = E/{3(I - 2v)}

This may be understood that elastic constants E and G are not determined from tension or torsion test since the machines for these tests undergo adjustment of clearance and also some deformation that is reflected in diagram ordinarily. The constants are determined from those devices, which display large deformation for comparatively smaller load. For example, E is determined by measuring deflection of a beam beneath a central load and G is determined by measuring deflection of a close-coiled helical spring under an axial load. Poisson's ratio is generally not measured directly although is calculated from above equation. The elastic constants keep fairly constant for a class of material and are independent of specimens.

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